Notes:
Infant Baptism Arguement: Baptism is the moment one becomes set apart into God's covenant community. Since the covenant sign was administered to infants during the times of the Old Testament, and since the New Testament does not mention that this norm should cease, then there is no good reason for Christians to withhold baptism from their babies.
Believer Baptism Arguement: Baptism is the moment one publicaly declares his or her faith in Jesus. Therefore, baptism should only be administered to believers. Since there is not a clear example or command in the New Testament to apply baptism to infants, there is no good reason to apply baptism to infants. As for the Old Testament reasoning: The old covenant sign of circumcision served as a reminder to Israel of how God blessed their father Abraham, making him and his descendents "fruitful". Circumcision also reminded God's people that the world's Savior would come from Israel/the line of Abramham (see Gen. 22:18). Thus, the old covenant sign declared what the Messiah will do - and this was applicable to all physical children of Abraham... But the new covenant sign (baptism) declares what the Messiah has done, and the benefits of what Christ has done is only applicable to the spiritual children of Abraham by faith.